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Review Articles

An Approach to Masonry Structural Analysis by the No-Tension Assumption—Part I: Material Modeling, Theoretical Setup, and Closed Form Solutions

[+] Author and Article Information
Alessandro Baratta

Department of Structural Engineering, University of Naples Federico II, Napoli 80125, Italyalessandro.baratta@unina.it

Ottavia Corbi

Department of Structural Engineering, University of Naples Federico II, Napoli 80125, Italyottavia.corbi@unina.it

Appl. Mech. Rev 63(4), 040802 (Jan 13, 2011) (17 pages) doi:10.1115/1.4002790 History: Received September 22, 2010; Revised October 14, 2010; Published January 13, 2011; Online January 13, 2011

The prevalent feature that characterizes masonry structures and makes them dissimilar from modern reinforced concrete and steel structures is quite definitely their inability to resist tensile stresses. Therefore, it is natural that the material model that is intended to be an “analog” of real masonry cannot resist tensile stress but possibly behaves elastically under pure compression, opening a perspective on the adoption of the no-tension (NT) material constitutive assumption. Founded on the NT theory, the basic direction and aim of the present work is to propose a unified treatment of masonry structures presenting an overall and comprehensive up-to-date insight in the analysis of masonry constructions while providing basic and advanced concepts and tools already available or original. The note is intended to lead to several notable results including, just to mention some of the outcomes, that the St. Venant’s postulate does not hold in NT solids, no energy is dissipated by fracture, special accommodations for discontinuous loads are needed, and the relevant developments are provided, among other significant outcomes such as the identification of operative procedures for engineering solutions of structural problems. In the first part of the paper, the basics for the foundation of a NT material theory are illustrated, and the relevant principles for structural analysis, mainly identified in the classic energy theorems and suitably adapted to the material at hand, are formulated. In (apparently) simple cases, closed-form solutions can be obtained, or, at least, the solution process can be prepared after a preliminary screening of the equilibrium scenario. The application to two-dimensional no-tension elasticity is then illustrated in the last section, with reference to two sample cases. The first example proves that the solution in a NT panel acted on by vertical loads on the top is clearly identified in terms of stress, but if discontinuities are present in the load pattern, these reflect in some strong singularities in the deformation field that requires to deepen the problem. The second example is concerned with a NT-elastic half-plane, and a technique to find approximate solutions is outlined and carried on in detail. In Part II of the note, it is demonstrated that discontinuous or lumped load patterns can be looked at as frontier cases: They are not in contrast, but in some sense they are not natural to NT solids. Still in Part II, it is shown how the equilibrium problem can be managed both through the strain and the stress approach.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) The stress vector ta acting on a generic surface element dΩa orthogonal to the direction “a” in a NT material and (b) the stress state on a material element with principal stress directions and components

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Figure 2

Admissible stress domains: (a) Indefinitely elastic behavior in compression Σ∗ and (b) plastic behavior in compression Σ∗p

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Figure 3

(a) Nonfractured layer and (b) fractured layer

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Figure 4

The relation between σ and εf: (a) σ<0 and (b) σ=0

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Figure 5

(a) The principal stress directions and components σx, σy, and τxy, (b) the fracture generation, and (c) the possible fracture velocities ds∗ related to the condition σ1=0

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Figure 6

The smooth approximation of fracture: (a) the material element and (b) the fracture strain pattern

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Figure 7

The stress and the fracture admissible domains: (a) Σ and Φ in the spaces of tensor components and (b) Σ∗ and the fracture Φ∗ in the spaces of principal components

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Figure 8

The reference NT-equilibrium problem

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Figure 9

The NT panel subject to loading conditions varying according to the factor multiplier λ

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Figure 10

The NT panel subject to loading conditions varying according to the load multipliers λi

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Figure 11

The NT beam-solid subject to two different force distributions burdening on its bases whose load resultants act in the z-direction and the relevant stress distributions in the interior of the solid: (a) Elastic material: At points at a distance larger than the “extinction length,” the stresses do not depend on the distribution of the tractions on the bases. (b) No-tension material: The stresses remain equal to the distribution of the tractions at all the cross sections.

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Figure 12

Solution search pattern: level curves of the objective function f(x) of the optimal problem under the constraints g1(x)≤0 and g2(x)≤0 and problem solution xo

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Figure 13

(a) The panel and the load pattern; ((b) and (c)) the equilibrium stress field

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Figure 14

(a) The deformation of the panel neglecting the elastic contribution and (b) Crushed stone specimens

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Figure 15

(a) The load pattern, (b) the elastic deformation (ν=0), and (c) the expected elastic and fractured deformation

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Figure 16

The NT-elastic semiplane with (a) the assumed load and (b) the stress diffusion pattern

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Figure 17

(a) Representation of αk(x) functions and its (b) first and (c) second derivatives for k=1,3,5

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Figure 18

The stress components along some horizontal and vertical fundamental lines: (a) σx, (b) σy, and (c) τxy

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